\De*gree"\, n. [F. degr['e], OF. degret, fr. LL.
degradare. See {Degrade}.]
1. A step, stair, or staircase. [Obs.]
By ladders, or else by degree. --Rom. of R.
2. One of a series of progressive steps upward or downward,
in quality, rank, acquirement, and the like; a stage in
progression; grade; gradation; as, degrees of vice and
virtue; to advance by slow degrees; degree of comparison.
3. The point or step of progression to which a person has
arrived; rank or station in life; position. ``A dame of
high degree.'' --Dryden. ``A knight is your degree.''
--Shak. ``Lord or lady of high degree.'' --Lowell.
4. Measure of advancement; quality; extent; as, tastes differ
in kind as well as in degree.
The degree of excellence which proclaims genius, is
different in different times and different places.
--Sir. J.
Reynolds.
5. Grade or rank to which scholars are admitted by a college
or university, in recognition of their attainments; as,
the degree of bachelor of arts, master, doctor, etc.
Note: In the United States diplomas are usually given as the
evidence of a degree conferred. In the humanities the
first degree is that of bachelor of arts (B. A. or A.
B.); the second that of master of arts (M. A. or A.
M.). The degree of bachelor (of arts, science,
divinity, law, etc.) is conferred upon those who
complete a prescribed course of undergraduate study.
The first degree in medicine is that of doctor of
medicine (M. D.). The degrees of master and doctor are
sometimes conferred, in course, upon those who have
completed certain prescribed postgraduate studies, as
doctor of philosophy (Ph. D.); but more frequently the
degree of doctor is conferred as a complimentary
recognition of eminent services in science or letters,
or for public services or distinction (as doctor of
laws (LL. D.) or doctor of divinity (D. D.), when they
are called honorary degrees.
The youth attained his bachelor's degree, and left the
university. --Macaulay.
6. (Genealogy) A certain distance or remove in the line of
descent, determining the proximity of blood; one remove in
the chain of relationship; as, a relation in the third or
fourth degree.
In the 11th century an opinion began to gain ground
in Italy, that third cousins might marry, being in
the seventh degree according to the civil law.
--Hallam.
7. (Arith.) Three figures taken together in numeration; thus,
140 is one degree, 222,140 two degrees.
8. (Algebra) State as indicated by sum of exponents; more
particularly, the degree of a term is indicated by the sum
of the exponents of its literal factors; thus, a^{2}b^{3}c
is a term of the sixth degree. The degree of a power, or
radical, is denoted by its index, that of an equation by
the greatest sum of the exponents of the unknown
quantities in any term; thus, ax^{4} + bx^{2} = c, and
mx^{2}y^{2} + nyx = p, are both equations of the fourth
degree.
9. (Trig.) A 360th part of the circumference of a circle,
which part is taken as the principal unit of measure for
arcs and angles. The degree is divided into 60 minutes and
the minute into 60 seconds.
10. A division, space, or interval, marked on a mathematical
or other instrument, as on a thermometer.
11. (Mus.) A line or space of the staff.
Note: The short lines and their spaces are added degrees.
{Accumulation of degrees}. (Eng. Univ.) See under
{Accumulation}.
{By degrees}, step by step; by little and little; by moderate
advances. ``I'll leave it by degrees.'' --Shak.
{Degree of a} {curve or surface} (Geom.), the number which
expresses the degree of the equation of the curve or
surface in rectilinear co["o]rdinates. A straight line
will, in general, meet the curve or surface in a number of
points equal to the degree of the curve or surface and no
more.
{Degree of latitude} (Geog.), on the earth, the distance on a
meridian between two parallels of latitude whose latitudes
differ from each other by one degree. This distance is not
the same on different parts of a meridian, on account of
the flattened figure of the earth, being 68.702 statute
miles at the equator, and 69.396 at the poles.
{Degree of longitude}, the distance on a parallel of latitude
between two meridians that make an angle of one degree
with each other at the poles -- a distance which varies as
the cosine of the latitude, being at the equator 69.16
statute miles.
{To a degree}, to an extreme; exceedingly; as, mendacious to
a degree.
It has been said that Scotsmen . . . are . . . grave
to a degree on occasions when races more favored by
nature are gladsome to excess. --Prof.
Wilson.

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Computing Dictionary

Definition:

The degree (or valency) of a node in a graph is the number of edges joined to it.